{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "28f576f6-4baf-4b3f-bf8c-680f0f21d04e",
   "metadata": {},
   "source": [
    "Chapter 19\n",
    "\n",
    "# 拟合圆\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4bc71154-8715-48e8-b778-e1c7cfb1b920",
   "metadata": {},
   "source": [
    "这段代码使用**最小二乘法**拟合一个二维平面上的圆，通过优化找到最佳圆心 $(x_c, y_c)$ 和半径 $R$，并通过可视化展示了散点数据和拟合结果。以下从数学角度详细描述代码的功能、数学公式以及可视化的目的。\n",
    "\n",
    "---\n",
    "\n",
    "### 1. **数学模型与目标**\n",
    "\n",
    "#### 圆的方程\n",
    "圆的标准方程为：\n",
    "$$\n",
    "(x - x_c)^2 + (y - y_c)^2 = R^2\n",
    "$$\n",
    "其中，$(x_c, y_c)$ 是圆心的坐标，$R$ 是半径。\n",
    "\n",
    "对于一组二维平面上的点 $(x_i, y_i)$，如果它们位于某个圆上，则应该满足上述方程。由于观测数据通常包含噪声，实际数据点 $(x_i, y_i)$ 与理想圆之间可能存在偏差。\n",
    "\n",
    "#### 拟合目标\n",
    "通过最小化残差定义的目标函数，找到最优的圆心 $(x_c, y_c)$ 和半径 $R$：\n",
    "1. 计算每个点 $(x_i, y_i)$ 到圆心 $(x_c, y_c)$ 的距离：\n",
    "   $$\n",
    "   R_i = \\sqrt{(x_i - x_c)^2 + (y_i - y_c)^2}\n",
    "   $$\n",
    "2. 定义残差为每个点的距离与平均半径 $R_\\text{mean}$ 的偏差：\n",
    "   $$\n",
    "   \\text{residual}(x_c, y_c) = R_i - R_\\text{mean}\n",
    "   $$\n",
    "3. 最小化所有残差的平方和：\n",
    "   $$\n",
    "   \\min_{x_c, y_c} \\sum_{i=1}^n \\left( R_i - R_\\text{mean} \\right)^2\n",
    "   $$\n",
    "\n",
    "代码通过 `leastsq` 实现了上述优化。\n",
    "\n",
    "---\n",
    "\n",
    "### 2. **数据生成**\n",
    "\n",
    "代码生成了一组近似分布在圆周上的散点数据，同时叠加了高斯噪声，以模拟实际观测中的误差：\n",
    "- 原始圆的中心为 $(50, 50)$，半径为 $40$；\n",
    "- 噪声为均值为 $0$，标准差为 $2$ 的正态分布。\n",
    "\n",
    "这组数据的分布近似形成一个圆，但不完全符合理想圆的方程。\n",
    "\n",
    "---\n",
    "\n",
    "### 3. **最小二乘拟合圆**\n",
    "\n",
    "#### 残差函数\n",
    "代码中的 `calc_R` 函数计算了每个点 $(x_i, y_i)$ 到假设圆心 $(x_c, y_c)$ 的距离：\n",
    "$$\n",
    "R_i = \\sqrt{(x_i - x_c)^2 + (y_i - y_c)^2}\n",
    "$$\n",
    "\n",
    "`residuals` 函数定义了优化目标的残差，即距离 $R_i$ 与平均距离 $R_\\text{mean}$ 的差：\n",
    "$$\n",
    "\\text{residuals}(x_c, y_c) = R_i - R_\\text{mean}, \\quad \\text{其中 } R_\\text{mean} = \\frac{1}{n} \\sum_{i=1}^n R_i\n",
    "$$\n",
    "\n",
    "#### 优化过程\n",
    "以散点的均值 $(x_m, y_m)$ 作为初始猜测的圆心，通过 `leastsq` 最小化残差平方和，找到最佳拟合的圆心 $(x_c, y_c)$ 和半径 $R$：\n",
    "$$\n",
    "(x_c, y_c) = \\arg\\min \\sum_{i=1}^n \\left( R_i - R_\\text{mean} \\right)^2\n",
    "$$\n",
    "\n",
    "优化后的圆心 $(x_c, y_c)$ 和平均半径 $R$ 描述了拟合的圆。\n",
    "\n",
    "---\n",
    "\n",
    "### 4. **可视化分析**\n",
    "\n",
    "#### 可视化 1：散点图\n",
    "第一张图绘制了原始散点数据，展示了点的近似圆周分布以及噪声对数据的影响。\n",
    "\n",
    "#### 可视化 2：伪圆心分析\n",
    "第二张图显示了一个假设的圆心 $(40, 60)$，并用直线连接该圆心和每个数据点 $(x_i, y_i)$。这些连线表明假设的圆心并不能很好地描述数据分布。\n",
    "\n",
    "#### 可视化 3：拟合圆\n",
    "第三张图绘制了通过最小二乘法拟合的圆：\n",
    "- 圆心 $(x_c, y_c)$ 用黑色叉标记；\n",
    "- 拟合圆的边界用红色绘制，半径为 $R$；\n",
    "- 蓝色散点表示原始数据点。\n",
    "\n",
    "图中可以直观地看到，拟合圆能够很好地描述散点的分布，表明最小二乘法有效地逼近了最佳圆。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5d4134c2-710a-4b6d-9eda-b3742567224c",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "849cd9ac-3a96-4eda-a5f7-1164abba4c49",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.optimize import leastsq"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5e9815ef-350c-4297-a1c2-899dc374187a",
   "metadata": {},
   "source": [
    "## 定义圆的残差函数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "0347f202-682c-4d50-80e3-a292056fed91",
   "metadata": {},
   "outputs": [],
   "source": [
    "def calc_R(xc, yc, x, y):\n",
    "    return np.sqrt((x - xc) ** 2 + (y - yc) ** 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "1899aca8-44ed-4b76-b81f-f3fe33d21be3",
   "metadata": {},
   "outputs": [],
   "source": [
    "def residuals(c, x, y):\n",
    "    xc, yc = c\n",
    "    Ri = calc_R(xc, yc, x, y)\n",
    "    return Ri - Ri.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "00923c46-1b9e-4c09-9788-b20869759091",
   "metadata": {},
   "source": [
    "## 生成近似圆的散点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "64333277-a491-4f32-83fe-aa9c1834863b",
   "metadata": {},
   "outputs": [],
   "source": [
    "np.random.seed(0)\n",
    "theta = np.linspace(0, 2 * np.pi, 10)\n",
    "x = 50 + 40 * np.cos(theta) + np.random.normal(0, 2, theta.size)\n",
    "y = 50 + 40 * np.sin(theta) + np.random.normal(0, 2, theta.size)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a5e5b8b6-285d-47ce-9929-abc983cb367e",
   "metadata": {},
   "source": [
    "## 初始估计的圆心"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "e1d88a43-edff-4d79-9f57-c0ad8fec6201",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_m, y_m = x.mean(), y.mean()\n",
    "initial_guess = [x_m, y_m]"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "f7196324-e286-45d6-b2d9-a7d685785340",
   "metadata": {},
   "source": [
    "## 使用最小二乘法拟合圆"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "867d2603-16ae-4208-8171-fd9af192ffce",
   "metadata": {},
   "outputs": [],
   "source": [
    "center_estimate, _ = leastsq(residuals, initial_guess, args=(x, y))\n",
    "xc, yc = center_estimate\n",
    "Ri = calc_R(xc, yc, x, y)\n",
    "R = Ri.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "983baf82-0661-4094-8b20-a7beac574dc5",
   "metadata": {},
   "source": [
    "## 可视化1：散点图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "4230de52-9e30-4d57-9e91-181545085b69",
   "metadata": {},
   "outputs": [
    {
     "data": {
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kpATuIyGFbrYcvCkzPT2wDvGJMgEAiKnU1MANqXp6hr780+2W6uoCRYJ7TMQvygQAIOZSU89dFri/RPxjzwQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsCTsZWLatGmy2WxDPlatWiVJMsbI4/HI5XIpKSlJhYWFamxsDHcMAAAQJWEvEw0NDTp69Gjww+v1SpLuvPNOSdLGjRu1adMmVVRUqKGhQU6nU0VFRerp6Ql3FAAAEAVhLxNXXHGFnE5n8OOVV17R9OnTVVBQIGOMysvLtW7dOi1evFgzZsxQZWWlent7VV1dHe4oAAAgCsZG8uT9/f3aunWrVq9eLZvNpqamJrW3t6u4uDi4xuFwqKCgQPX19VqxYsWw5/H5fPL5fMHj7u5uSZLf75ff74/kQwi7gbzkjg5yR1ei5pYSNzu5oyvRc0eKzRhjInXy//iP/1BJSYkOHz4sl8ul+vp65efnq62tTS6XK7hu+fLlOnTokGpqaoY9j8fj0fr164eMV1dXKzk5OVLxAQAYFXp7e1VSUqKuri5NnDgx7OeP6JWJ5557TvPnzw8pDpJks9lCjo0xQ8YGW7t2rVavXh087u7ultvt1ty5c5WWlhbe0BHm9/vl9XpVVFQku90e6zgjRu7oInf0JWp2ckdXouY+duxYRM8fsTJx6NAhvfbaa3rxxReDY06nU5LU3t6uzMzM4HhHR4cyMjLOeS6HwyGHwzFk3G63J9QPc7BEzU7u6CJ39CVqdnJHV6LljnTWiN1nYsuWLUpPT9fChQuDY9nZ2XI6ncFXeEiBfRV1dXXKy8uLVBQAABBBEbkycfr0aW3ZskVLly7V2LFnvoXNZlNpaanKysqUm5ur3NxclZWVKTk5WSUlJZGIAgAAIiwiZeK1117T4cOHtWzZsiFza9asUV9fn1auXKnOzk7Nnj1btbW1SklJiUQUAAAQYREpE8XFxTrXi0RsNps8Ho88Hk8kvjUAAIgy3psDAABYQpkAAACWUCYAAIAllAkAAGAJZQIAAFhCmQAAAJZQJgAAgCWUCQAAYAllAgAAWEKZAAAAllAmAACAJZQJAABgCWUCAABYQpkYhbq6pNbW4edaWwPzAACEC2VilOnqkubNkwoKpJaW0LmWlsD4vHkUCgBA+FAmRpmeHqmjQ2pqkgoLzxSKlpbAcVNTYL6nJ5YpAQCjCWVilMnKknbtknJyzhSK+vozRSInJzCflRXbnACA0WNsrAMg/NzuQGEYKBD5+YHxgSLhdscwHABg1OHKxCjldktVVaFjVVUUCQBA+FEmRqmWFmnJktCxJUuGbsoEAMAqysQoNHizZU6O9OaboXsoKBQAgHCiTIwyra1DN1vm5Q3dlHmu+1AAAHC+2IA5yqSkSOnpgT8P3mw5eFNmenpgHQAA4UCZGGVSU6WdOwP3kTj75Z9ut1RXFygSqamxyQcAGH0oE6NQauq5ywL3lwAAhBt7JgAAgCWUCQAAYAllAgAAWEKZAAAAllAmAACAJZQJAABgCWUCAABYQpkAAACWUCYAAIAllAkAAGBJRMpEW1ubvvGNbygtLU3Jycn6/Oc/rz179gTnjTHyeDxyuVxKSkpSYWGhGhsbIxEFAABEWNjLRGdnp/Lz82W32/Xqq6/qt7/9rf7+7/9en/nMZ4JrNm7cqE2bNqmiokINDQ1yOp0qKipST09PuOMAAIAIC/sbfT311FNyu93asmVLcGzatGnBPxtjVF5ernXr1mnx4sWSpMrKSmVkZKi6ulorVqwIdyQAABBBYS8TL7/8sm699Vbdeeedqqur0+TJk7Vy5Up95zvfkSQ1Nzervb1dxcXFwa9xOBwqKChQfX39sGXC5/PJ5/MFj7u7uyVJfr9ffr8/3A8hogbykjs6yB1diZpbStzs5I6uRM8dKTZjjAnnCcePHy9JWr16te688069/fbbKi0t1b/+67/qvvvuU319vfLz89XW1iaXyxX8uuXLl+vQoUOqqakZck6Px6P169cPGa+urlZycnI44wMAMOr09vaqpKREXV1dmjhxYtjPH/YrE6dPn9asWbNUVlYmSbrhhhvU2NiozZs367777guus9lsIV9njBkyNmDt2rVavXp18Li7u1tut1tz585VWlpauB9CRPn9fnm9XhUVFclut8c6zoiRO7rIHX2Jmp3c0ZWouY8dOxbR84e9TGRmZuqaa64JGbv66qv1wgsvSJKcTqckqb29XZmZmcE1HR0dysjIGPacDodDDodjyLjdbk+oH+ZgiZqd3NFF7uhL1Ozkjq5Eyx3prGF/NUd+fr4OHDgQMvbBBx9o6tSpkqTs7Gw5nU55vd7gfH9/v+rq6pSXlxfuOAAAIMLCfmXiu9/9rvLy8lRWVqa77rpLb7/9tp555hk988wzkgK/3igtLVVZWZlyc3OVm5ursrIyJScnq6SkJNxxAABAhIW9THzxi1/U9u3btXbtWj322GPKzs5WeXm57r333uCaNWvWqK+vTytXrlRnZ6dmz56t2tpapaSkhDsOAACIsLCXCUm67bbbdNttt51z3mazyePxyOPxROLbAwCAKOK9OQAAgCWUCQAAYAllAgAAWEKZAAAAllAmAACAJZQJAABgCWUCAABYQpkAAACWUCYAAIAllAkAAGAJZQIAAFhCmQAAAJZQJgAAgCWUCQAAYAllAgAAWEKZAAAAllAmAACAJZQJAABgCWUCAABYQpkAAACWUCYAAIAllAkAAGAJZQIAAFhCmQAAAJZQJgAAgCWUCQAAYAllAgAAWEKZAAAAllAmAACAJZQJAABgCWUCAABYQpkAAACWUCYAAIAllAkAACKoq0tqbR1+rrU1MJ/oKBMAAERIV5c0b55UUCC1tITOtbQExufNS/xCEfYy4fF4ZLPZQj6cTmdw3hgjj8cjl8ulpKQkFRYWqrGxMdwxAACIuZ4eqaNDamqSCgvPFIqWlsBxU1Ngvqcnlimti8iViWuvvVZHjx4Nfuzfvz84t3HjRm3atEkVFRVqaGiQ0+lUUVGRehL9mQQA4CxZWdKuXVJOzplCUV9/pkjk5ATms7Jim9OqiJSJsWPHyul0Bj+uuOIKSYGrEuXl5Vq3bp0WL16sGTNmqLKyUr29vaquro5EFAAAYsrtDi0U+fmhRcLtjnVC68ZG4qQffvihXC6XHA6HZs+erbKyMuXk5Ki5uVnt7e0qLi4OrnU4HCooKFB9fb1WrFgx7Pl8Pp98Pl/wuLu7W5Lk9/vl9/sj8RAiZiAvuaOD3NGVqLmlxM1O7ui60NxOp1RZKQ3650+VlYHxaDwFkX6ebcYYE84Tvvrqq+rt7dWVV16p3//+93r88cf1u9/9To2NjTpw4IDy8/PV1tYml8sV/Jrly5fr0KFDqqmpGfacHo9H69evHzJeXV2t5OTkcMYHAGDU6e3tVUlJibq6ujRx4sSwnz/sZeJsJ0+e1PTp07VmzRp9+ctfVn5+vo4cOaLMzMzgmu985ztqaWnRzp07hz3HcFcm3G63jh49qrS0tEjGDzu/3y+v16uioiLZ7fZYxxkxckcXuaMvUbOTO7ouJHdbm7RggXTwoDRtmvTMM9Ly5WeOd+yQJk+OYGhJx44dU2ZmZsTKRER+zTHYhAkTdN111+nDDz/UHXfcIUlqb28PKRMdHR3KyMg45zkcDoccDseQcbvdnlB/CQdL1Ozkji5yR1+iZid3dI00d2urdPPNZ/ZI1NQE9kjU1AQ2Yb7/fmC+ri6ymzAj/RxH/D4TPp9P77//vjIzM5WdnS2n0ymv1xuc7+/vV11dnfLy8iIdBQCAsDhyZPjxs29ClZIipacP3Ww5eFNmenpgXSIL+5WJ73//+7r99ts1ZcoUdXR06PHHH1d3d7eWLl0qm82m0tJSlZWVKTc3V7m5uSorK1NycrJKSkrCHQUAgLD6v/3/mj//zFWGAQP3jkhPl3bulFJTAx87dwbuI3H2lQe3O3BFIiUlsC6Rhb1MtLa26p577tEf/vAHXXHFFfryl7+st956S1OnTpUkrVmzRn19fVq5cqU6Ozs1e/Zs1dbWKiXRaxkAYNQ7cSLw+eDBQHEYuNow+CZUUqA8DBSEgVIxnES/v8SAsJeJbdu2/cl5m80mj8cjj8cT7m8NAEBEuVzSvn2BjZPvvx8oEFVV0pIlo+smVOcr4hswAQAYbXbsOLOxMj8/MDaabkJ1vnijLwAAztPkyYErEoNVVV2cRUKiTAAAcN7a2gK/2hhsyZKh7wx6saBMAABwnhYsOLNH4s03Q9/I62IsFJQJAABGaOD+EgcPntkjkZc39J1BW1tjlzEWKBMAAIzQpZcGPk+bNrpvQnW+eDUHAAAjNPC2Fq++OnSz5Wi6CdX5okwAAHCeBr3xdYiL7f4SA/g1BwAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASyJeJjZs2CCbzabS0tLgmDFGHo9HLpdLSUlJKiwsVGNjY6SjAACACIhomWhoaNAzzzyj66+/PmR848aN2rRpkyoqKtTQ0CCn06mioiL19PREMg4AAIiAiJWJEydO6N5779Wzzz6ryy67LDhujFF5ebnWrVunxYsXa8aMGaqsrFRvb6+qq6sjFQcAAETI2EideNWqVVq4cKFuueUWPf7448Hx5uZmtbe3q7i4ODjmcDhUUFCg+vp6rVixYsi5fD6ffD5f8Li7u1uS5Pf75ff7I/UQImIgL7mjg9zRlai5pcTNTu7oSvTckRKRMrFt2zbt3btXDQ0NQ+ba29slSRkZGSHjGRkZOnTo0LDn27Bhg9avXz9k/PXXX1dycnIYEkef1+uNdYQLQu7oInf0JWp2ckdXouXu7e2N6PnDXiZaWlr00EMPqba2VuPHjz/nOpvNFnJsjBkyNmDt2rVavXp18Li7u1tut1tz585VWlpaeIJHid/vl9frVVFRkex2e6zjjBi5o4vc0Zeo2ckdXYma+9ixYxE9f9jLxJ49e9TR0aEbb7wxOHbq1Cm98cYbqqio0IEDByQFrlBkZmYG13R0dAy5WjHA4XDI4XAMGbfb7Qn1wxwsUbOTO7rIHX2Jmp3c0ZVouSOdNewbMG+++Wbt379f+/btC37MmjVL9957r/bt26ecnBw5nc6QS0T9/f2qq6tTXl5euOMAAIAIC/uViZSUFM2YMSNkbMKECUpLSwuOl5aWqqysTLm5ucrNzVVZWZmSk5NVUlIS7jgAACDCIvZqjj9lzZo16uvr08qVK9XZ2anZs2ertrZWKSkpsYgDAAAsiEqZ2LVrV8ixzWaTx+ORx+OJxrcHAAARxHtzAAAASygTAADAEspEFHV1SUeODD/X2hqYBwAg0VAmoqSrS5o3T5o/f+hcS4tUUBCYp1AAABINZSJKenqkjg7p4MHAcVtb4HNLi1RYKDU1BeZ541QAQKKhTERJVpa0a5c0bVrgeMECqb7+TJHIyQnMZ2XFLiMAABeCMhFFbre0Y0fgzwcPSvn5oUXC7Y5lOgAALgxlIsomTx46VlVFkQAAJC7KRJQN7JUYbMmSwN4JAAASEWUiilpaAnslpMDeiTffDPyKo6kpsHeCQgEASESUiShpbQ0UhoFXc+zYIeXlBfZKDC4Ura2xywgAwIWgTERJSoqUnn7m1RwDeyfc7jOFIj09sA4AgEQSk3cNvRilpko7d0rHj0v79oXOud1SXV2gSKSmxiIdAAAXjisTUZSaKrlcw89lZVEkAACJiTIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALAl7mdi8ebOuv/56TZw4URMnTtScOXP06quvBueNMfJ4PHK5XEpKSlJhYaEaGxvDHQMAAERJ2MtEVlaWnnzySb3zzjt655139NWvflWLFi0KFoaNGzdq06ZNqqioUENDg5xOp4qKitTT0xPuKAAAIArCXiZuv/12LViwQFdeeaWuvPJKPfHEE7r00kv11ltvyRij8vJyrVu3TosXL9aMGTNUWVmp3t5eVVdXhzsKAACIgojumTh16pS2bdumkydPas6cOWpublZ7e7uKi4uDaxwOhwoKClRfXx/JKAAAIELGRuKk+/fv15w5c/THP/5Rl156qbZv365rrrkmWBgyMjJC1mdkZOjQoUPnPJ/P55PP5wsed3d3S5L8fr/8fn8EHkHkDOQld3SQO7oSNbeUuNnJHV2JnjtSbMYYE+6T9vf36/Dhwzp+/LheeOEF/eQnP1FdXZ2OHz+u/Px8HTlyRJmZmcH13/nOd9TS0qKdO3cOez6Px6P169cPGa+urlZycnK44wMAMKr09vaqpKREXV1dmjhxYtjPH5EycbZbbrlF06dP18MPP6zp06dr7969uuGGG4LzixYt0mc+8xlVVlYO+/XDXZlwu906evSo0tLSIh0/rPx+v7xer4qKimS322MdZ8TIHV3kjr5EzU7u6ErU3MeOHVNmZmbEykREfs1xNmOMfD6fsrOz5XQ65fV6g2Wiv79fdXV1euqpp8759Q6HQw6HY8i43W5PqB/mYImandzRRe7oS9Ts5I6uRMsd6axhLxM//OEPNX/+fLndbvX09Gjbtm3atWuXdu7cKZvNptLSUpWVlSk3N1e5ubkqKytTcnKySkpKwh0FAABEQdjLxO9//3stWbJER48eVWpqqq6//nrt3LlTRUVFkqQ1a9aor69PK1euVGdnp2bPnq3a2lqlpKSEOwoAAIiCsJeJ55577k/O22w2eTweeTyecH9rAAAQA7w3BwAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAgqrq6pCNHhp9rbQ3MI7FQJgAAUdPVJc2bJ82fP3SupUUqKAjMUygSC2UCABA1PT1SR4d08GDguK0t8LmlRSoslJqaAvM9PbFKiAtBmQAARE1WlrRrlzRtWuB4wQKpvv5MkcjJCcxnZcUuI84fZQIAEFVut7RjR+DPBw9K+fmhRcLtjmU6XAjKBAAg6iZPHjpWVUWRSFSUCQBA1A3slRhsyZLA3gkkHsoEACCqWloCeyWkwN6JN98M/IqjqSmwd4JCkXgoEwCAqGltDRSGgVdz7Ngh5eUF9koMLhStrbHLiPNHmQAARE1KipSefubVHAN7J9zuM4UiPT2wDoljbKwDAAAuHqmp0s6d0vHj0r59oXNut1RXFygSqamxSIcLxZUJAEBUpaZKLtfwc1lZFIlERJkAAACWUCYAAIAllAkAAGAJZQIAAFhCmQAAAJZQJgAAgCWUCQAAYAllAgAAWEKZAAAAllAmAACAJZQJAABgCWUCAABYEvYysWHDBn3xi19USkqK0tPTdccdd+jAgQMha4wx8ng8crlcSkpKUmFhoRobG8MdBQAAREHYy0RdXZ1WrVqlt956S16vV5988omKi4t18uTJ4JqNGzdq06ZNqqioUENDg5xOp4qKitTT0xPuOAAAIMLGhvuEO3fuDDnesmWL0tPTtWfPHn3lK1+RMUbl5eVat26dFi9eLEmqrKxURkaGqqurtWLFinBHAgAAERT2MnG2rq4uSdKkSZMkSc3NzWpvb1dxcXFwjcPhUEFBgerr64ctEz6fTz6fL3jc3d0tSfL7/fL7/ZGMH3YDeckdHeSOrkTNLSVudnJHV6LnjhSbMcZE6uTGGC1atEidnZ365S9/KUmqr69Xfn6+2tra5HK5gmuXL1+uQ4cOqaamZsh5PB6P1q9fP2S8urpaycnJkYoPAMCo0Nvbq5KSEnV1dWnixIlhP39Er0w88MAD+s1vfqPdu3cPmbPZbCHHxpghYwPWrl2r1atXB4+7u7vldrs1d+5cpaWlhTd0hPn9fnm9XhUVFclut8c6zoiRO7rIHX2Jmp3c0ZWouY8dOxbR80esTDz44IN6+eWX9cYbbygrKys47nQ6JUnt7e3KzMwMjnd0dCgjI2PYczkcDjkcjiHjdrs9oX6YgyVqdnJHF7mjL1Gzkzu6Ei13pLOG/dUcxhg98MADevHFF/WLX/xC2dnZIfPZ2dlyOp3yer3Bsf7+ftXV1SkvLy/ccYBhdXVJra3Dz7W2BuYBACMT9isTq1atUnV1tf7rv/5LKSkpam9vlySlpqYqKSlJNptNpaWlKisrU25urnJzc1VWVqbk5GSVlJSEOw4wRFeXNG+e1NEh7dolud1n5lpapMJCKT1d2rlTSk2NVUoASBxhLxObN2+WJBUWFoaMb9myRd/85jclSWvWrFFfX59Wrlypzs5OzZ49W7W1tUpJSQl3HGCInp5AkWhqChSHgUIxUCSams6so0wAwKcLe5kYyYtDbDabPB6PPB5PuL898KmysgIFYqA4FBZKVVXSkiWB45ycwPygrT4AgD8h4veZAOKR2x1aKPLzA+MDRWLwrz4AAH8ab/SFi5bbHbgiMVhVFUUCAM4XZQIXrZaWwK82BluyJDAOABg5ygQuSoM3W+bkSG++Gfg8sIeCQgEAI0eZwEWntTW0SOzaJeXlBT4PLhTnug8FACAUGzBx0UlJCdxHQgrdbDl4U2Z6emAdAODTUSZw0UlNDdyQqqdn6Ms/3W6pri5QJLjHBACMDGUCF6XU1HOXBe4vAQDnhz0TAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEgITV1SW1tg4/19oamAcQeZQJAAmpq0uaN08qKJBaWkLnWloC4/PmUSiAaAh7mXjjjTd0++23y+VyyWaz6aWXXgqZN8bI4/HI5XIpKSlJhYWFamxsDHcMAKNcT4/U0SE1NUmFhWcKRUtL4LipKTDf0xPLlMDFIexl4uTJk5o5c6YqKiqGnd+4caM2bdqkiooKNTQ0yOl0qqioSD38Fw/gPGRlSbt2STk5ZwpFff2ZIpGTE5jPyoptTuBiMDbcJ5w/f77mz58/7JwxRuXl5Vq3bp0WL14sSaqsrFRGRoaqq6u1YsWKcMcBMIq53YHCMFAg8vMD4wNFwu2OYTjgIhL2MvGnNDc3q729XcXFxcExh8OhgoIC1dfXn7NM+Hw++Xy+4HF3d7ckye/3y+/3RzZ0mA3kJXd0kDu6YpHb6ZQqK6VB/7OiysrA+PnE4DmPLnJHV6Tz2owxJmInt9m0fft23XHHHZKk+vp65efnq62tTS6XK7hu+fLlOnTokGpqaoY9j8fj0fr164eMV1dXKzk5OSLZAQAYLXp7e1VSUqKuri5NnDgx7OeP6pWJATabLeTYGDNkbLC1a9dq9erVwePu7m653W7NnTtXaWlpEcsZCX6/X16vV0VFRbLb7bGOM2Lkji5yj0xbm7RggXTwoDRtmvTMM9Ly5WeOd+yQJk8e2bl4zqOL3NF17NixiJ4/qmXC6XRKktrb25WZmRkc7+joUEZGxjm/zuFwyOFwDBm32+0J9cMcLFGzkzu6yH1ura3SzTef2WxZUxPYI1FTE9hD8f77gfm6uvPbhMlzHl3kjo5IZ43qfSays7PldDrl9XqDY/39/aqrq1NeXl40owBIcCkpUnr60M2WA5syc3IC8ykpsUwJXBzCfmXixIkT+uijj4LHzc3N2rdvnyZNmqQpU6aotLRUZWVlys3NVW5ursrKypScnKySkpJwRwEwiqWmSjt3Bu4jcfaVB7c7cEUiJSWwDkBkhb1MvPPOO5o7d27weGCvw9KlS/XTn/5Ua9asUV9fn1auXKnOzk7Nnj1btbW1SuH/PgA4T6mp5y4L3F8CiJ6wl4nCwkL9qReI2Gw2eTweeTyecH9rAAAQA7w3BwAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACwhDIBAAAsoUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEtiWib+5V/+RdnZ2Ro/frxuvPFG/fKXv4xlHAAAcAFiViaef/55lZaWat26dXr33Xf1Z3/2Z5o/f74OHz4cq0gAAOACxKxMbNq0Sd/61rf07W9/W1dffbXKy8vldru1efPmWEUCAAAXYGwsvml/f7/27NmjRx55JGS8uLhY9fX1Q9b7fD75fL7gcVdXlyTp448/jmzQCPD7/ert7dWxY8dkt9tjHWfEyB1d5I6+RM1O7uhK1NwD/14aYyJy/piUiT/84Q86deqUMjIyQsYzMjLU3t4+ZP2GDRu0fv36IeNXXnllxDICADDaHDt2TKmpqWE/b0zKxACbzRZybIwZMiZJa9eu1erVq4PHx48f19SpU3X48OGIPCmR1N3dLbfbrZaWFk2cODHWcUaM3NFF7uhL1Ozkjq5Ezd3V1aUpU6Zo0qRJETl/TMrE5ZdfrjFjxgy5CtHR0THkaoUkORwOORyOIeOpqakJ9cMcbOLEiQmZndzRRe7oS9Ts5I6uRM19ySWR2SoZkw2Y48aN04033iiv1xsy7vV6lZeXF4tIAADgAsXs1xyrV6/WkiVLNGvWLM2ZM0fPPPOMDh8+rPvvvz9WkQAAwAWIWZm4++67dezYMT322GM6evSoZsyYoR07dmjq1Kmf+rUOh0OPPvrosL/6iHeJmp3c0UXu6EvU7OSOLnIPz2Yi9ToRAABwUeC9OQAAgCWUCQAAYAllAgAAWEKZAAAAliRkmYj3ty5/4403dPvtt8vlcslms+mll14KmTfGyOPxyOVyKSkpSYWFhWpsbIxN2EE2bNigL37xi0pJSVF6erruuOMOHThwIGRNPGbfvHmzrr/++uBNZObMmaNXX301OB+PmYezYcMG2Ww2lZaWBsfiNbvH45HNZgv5cDqdwfl4zS1JbW1t+sY3vqG0tDQlJyfr85//vPbs2ROcj8fs06ZNG/J822w2rVq1Km4zS9Inn3yiH/3oR8rOzlZSUpJycnL02GOP6fTp08E18Zq9p6dHpaWlmjp1qpKSkpSXl6eGhobgfLzkDse/Nz6fTw8++KAuv/xyTZgwQV/72tfU2tp6fkFMgtm2bZux2+3m2WefNb/97W/NQw89ZCZMmGAOHToU62hBO3bsMOvWrTMvvPCCkWS2b98eMv/kk0+alJQU88ILL5j9+/ebu+++22RmZpru7u7YBP4/t956q9myZYt57733zL59+8zChQvNlClTzIkTJ4Jr4jH7yy+/bP7nf/7HHDhwwBw4cMD88Ic/NHa73bz33ntxm/lsb7/9tpk2bZq5/vrrzUMPPRQcj9fsjz76qLn22mvN0aNHgx8dHR3B+XjN/fHHH5upU6eab37zm+ZXv/qVaW5uNq+99pr56KOPgmviMXtHR0fIc+31eo0k8/rrr8dtZmOMefzxx01aWpp55ZVXTHNzs/nP//xPc+mll5ry8vLgmnjNftddd5lrrrnG1NXVmQ8//NA8+uijZuLEiaa1tTWucofj35v777/fTJ482Xi9XrN3714zd+5cM3PmTPPJJ5+MOEfClYkvfelL5v777w8Zu+qqq8wjjzwSo0R/2tk/3NOnTxun02mefPLJ4Ngf//hHk5qaan784x/HIOG5dXR0GEmmrq7OGJNY2S+77DLzk5/8JCEy9/T0mNzcXOP1ek1BQUGwTMRz9kcffdTMnDlz2Ll4zv3www+bm2666Zzz8Zx9sIceeshMnz7dnD59Oq4zL1y40CxbtixkbPHixeYb3/iGMSZ+n+/e3l4zZswY88orr4SMz5w506xbty5uc1/IvzfHjx83drvdbNu2Lbimra3NXHLJJWbnzp0j/t4J9WuOgbcuLy4uDhk/11uXx6Pm5ma1t7eHPAaHw6GCgoK4ewwDb/U+8MYwiZD91KlT2rZtm06ePKk5c+YkROZVq1Zp4cKFuuWWW0LG4z37hx9+KJfLpezsbH39619XU1OTpPjO/fLLL2vWrFm68847lZ6erhtuuEHPPvtscD6esw/o7+/X1q1btWzZMtlstrjOfNNNN+nnP/+5PvjgA0nSr3/9a+3evVsLFiyQFL/P9yeffKJTp05p/PjxIeNJSUnavXt33OY+20hy7tmzR36/P2SNy+XSjBkzzuuxJFSZON+3Lo9HAznj/TEYY7R69WrddNNNmjFjhqT4zr5//35deumlcjgcuv/++7V9+3Zdc801cZ1ZkrZt26a9e/dqw4YNQ+biOfvs2bP1s5/9TDU1NXr22WfV3t6uvLw8HTt2LK5zNzU1afPmzcrNzVVNTY3uv/9+/fVf/7V+9rOfSYrv53zASy+9pOPHj+ub3/ympPjO/PDDD+uee+7RVVddJbvdrhtuuEGlpaW65557JMVv9pSUFM2ZM0d/+7d/qyNHjujUqVPaunWrfvWrX+no0aNxm/tsI8nZ3t6ucePG6bLLLjvnmpGI6VuQX6iRvnV5PIv3x/DAAw/oN7/5jXbv3j1kLh6zf+5zn9O+fft0/PhxvfDCC1q6dKnq6uqC8/GYuaWlRQ899JBqa2uH/D+gweIx+/z584N/vu666zRnzhxNnz5dlZWV+vKXvywpPnOfPn1as2bNUllZmSTphhtuUGNjozZv3qz77rsvuC4esw947rnnNH/+fLlcrpDxeMz8/PPPa+vWraqurta1116rffv2qbS0VC6XS0uXLg2ui8fsVVVVWrZsmSZPnqwxY8boC1/4gkpKSrR3797gmnjMPZwLyXm+jyWhrkyc71uXx6OBHe/x/BgefPBBvfzyy3r99deVlZUVHI/n7OPGjdNnP/tZzZo1Sxs2bNDMmTP1j//4j3Gdec+ePero6NCNN96osWPHauzYsaqrq9M//dM/aezYscF88Zj9bBMmTNB1112nDz/8MK6f88zMTF1zzTUhY1dffbUOHz4sKb7/jkvSoUOH9Nprr+nb3/52cCyeM//gBz/QI488oq9//eu67rrrtGTJEn33u98NXomL5+zTp09XXV2dTpw4oZaWFr399tvy+/3Kzs6O69yDjSSn0+lUf3+/Ojs7z7lmJBKqTIyGty4f+Is4+DH09/errq4u5o/BGKMHHnhAL774on7xi18oOzs7ZD6es5/NGCOfzxfXmW+++Wbt379f+/btC37MmjVL9957r/bt26ecnJy4zX42n8+n999/X5mZmXH9nOfn5w95ufMHH3wQfIPBeM4uSVu2bFF6eroWLlwYHIvnzL29vbrkktB/ZsaMGRN8aWg8Zx8wYcIEZWZmqrOzUzU1NVq0aFFC5JZG9vzeeOONstvtIWuOHj2q99577/weywVsGI2pgZeGPvfcc+a3v/2tKS0tNRMmTDAHDx6MdbSgnp4e8+6775p3333XSDKbNm0y7777bvDlq08++aRJTU01L774otm/f7+555574uKlUH/1V39lUlNTza5du0Jehtbb2xtcE4/Z165da9544w3T3NxsfvOb35gf/vCH5pJLLjG1tbVxm/lcBr+aw5j4zf69733P7Nq1yzQ1NZm33nrL3HbbbSYlJSX432G85n777bfN2LFjzRNPPGE+/PBD82//9m8mOTnZbN26NbgmXrOfOnXKTJkyxTz88MND5uI189KlS83kyZODLw198cUXzeWXX27WrFkTXBOv2Xfu3GleffVV09TUZGpra83MmTPNl770JdPf3x9XucPx7839999vsrKyzGuvvWb27t1rvvrVr47+l4YaY8w///M/m6lTp5px48aZL3zhC8GXLsaL119/3Uga8rF06VJjTODlOo8++qhxOp3G4XCYr3zlK2b//v2xDW3MsJklmS1btgTXxGP2ZcuWBf8+XHHFFebmm28OFglj4jPzuZxdJuI1+8Br1e12u3G5XGbx4sWmsbExOB+vuY0x5r//+7/NjBkzjMPhMFdddZV55plnQubjNXtNTY2RZA4cODBkLl4zd3d3m4ceeshMmTLFjB8/3uTk5Jh169YZn88XXBOv2Z9//nmTk5Njxo0bZ5xOp1m1apU5fvx4cD5ecofj35u+vj7zwAMPmEmTJpmkpCRz2223mcOHD59XDt6CHAAAWJJQeyYAAED8oUwAAABLKBMAAMASygQAALCEMgEAACyhTAAAAEsoEwAAwBLKBAAAsIQyAQAALKFMAAAASygTAADAEsoEAACw5P8DN8CSMam9CoYAAAAASUVORK5CYII=",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.scatter(x, y, marker = 'x', \n",
    "            color='blue', label=\"Data Points\")\n",
    "\n",
    "plt.ylim(0,100)\n",
    "plt.xlim(0,100)\n",
    "plt.xticks(np.arange(0,110,10))\n",
    "plt.yticks(np.arange(0,110,10))\n",
    "plt.grid()\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "cac07ed7-30fe-4631-8358-0c627dc68a91",
   "metadata": {},
   "source": [
    "# 可视化2：伪圆心"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "29fa17ff-d680-4fa9-87a6-5f5616709db5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.scatter(x, y, marker = 'x', \n",
    "            color='blue', label=\"Data Points\")\n",
    "plt.scatter(40,60,marker = 'x',color = 'k', s = 100)\n",
    "for x_i,y_i in zip(x,y):\n",
    "    plt.plot((40,x_i),(60,y_i), color = 'k')\n",
    "plt.ylim(0,100)\n",
    "plt.xlim(0,100)\n",
    "plt.xticks(np.arange(0,110,10))\n",
    "plt.yticks(np.arange(0,110,10))\n",
    "plt.grid()\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "817b7d96-327f-4ece-93b9-08428283ec56",
   "metadata": {},
   "source": [
    "# 可视化3：拟合圆"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "a053d6cf-0e07-4357-9137-1cd8d57fcff9",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 800x600 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(figsize=(8, 6))\n",
    "plt.scatter(x, y, marker = 'x', \n",
    "            color='blue', label=\"Data Points\")\n",
    "# 绘制拟合圆\n",
    "circle = plt.Circle((xc, yc), R, color='red', fill=False, label=\"Fitted Circle\")\n",
    "ax.add_artist(circle)\n",
    "# 绘制圆心\n",
    "ax.plot(xc, yc, 'x', label=\"Center\", color='black', markersize=10)\n",
    "\n",
    "# plt.legend()\n",
    "plt.ylim(0,100)\n",
    "plt.xlim(0,100)\n",
    "plt.xticks(np.arange(0,110,10))\n",
    "plt.yticks(np.arange(0,110,10))\n",
    "plt.grid()\n",
    "ax.set_aspect('equal', adjustable='box')\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.12.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}
